December 6: Michael McBreen

Title: C*-equivariant Homological Mirror Symmetry for Hypertoric Varieties

Abstract:

Hypertoric varieties are basic examples of symplectic resolutions, a class of algebraic symplectic varieties which plays a key role in contemporary geometric representation theory. I will discuss joint work with Ben Webster, which constructs a derived equivalence between C*-equivariant coherent sheaves on a hypertoric variety (the 'B-model') and a category of microlocal sheaves on a multiplicative hypertoric variety (the 'A-model'), and explain how this relates to the usual formulation of mirror symmetry. I will give special attention to the notion of microlocal Hodge structure on the A-model, which reproduces the C*-action on the B-model. All of this will be served as a bite-sized nugget, by focusing on the case of T*P^1.